Chapter 9: How the universe demands mathematical rules especially powers of 2.

Powers of Two in Operation

For a moment, we will step into the conventional world and speak of the superforce in its normal sense. Gravity.

Science students learn the gravitational formula for how two objects attract one another. Despising that word “attract” used with regards to gravity, we will suspend that spite temporarily.

For those unfamiliar with, or those having faded memories of, the formula appears below.

where F is force in Newtons, G is the universal gravitational constant, M is mass of object 1, m is mass of object 2, and r is the radius or distance between the objects’ centers of mass.

The objective of this topic is not to review the formula but to describe why the force varies inversely as the square of the distance between. Why is it the square of the distance instead of 1.810 times the distance or 5.815 times the distance? Or for that matter, why it isn’t any one of the other infinite number of choices? It is because our Universe demands rationality and stability. Earlier on, we mentioned the universe adopting the number two as a stabilizing quantity. It reflects a binary choice, yes-no, on-off, one-zero, but never maybe. Maybes turn into failed particles. Maybes turn into dark matter.

Using the similarity rule for triangles where all angles remain the same, the ratio of its sides remain the same. See Angle 1. Here a small triangle is superimposed on a larger similar triangle. At distance d, height h is fifty meters. At distance d/2, the height h/2 has been cut in half to twenty-five meters.

The same is true for heavenly bodies.

This requires another picture, an imaginary view of a distance object, even a pinpoint works. The imagination part is visualizing the superforce vectors coming directly at you from a great distance. They come at you surrounding the object and through the object in question.

The perspectives of Angle 1 must be reversed for this to work because the object needs to grow as it approaches the observer instead of contracting as the distance increases. That is, the physical size of the object remains the same, but its arc increases. It takes up more of the sky as it comes closer.

There are two representations of our distant object. One is image Head-On as it appears to flux detecting goggles, the other a profile as in Angle 2. Say it is an asteroid, a large one, perhaps large enough to be round. A radar observer first spots it at some point in the sky when it’s just a blip on her screen. That point is z shown on Angle 2. The astronomer researches the blip and discovers there is no history. It’s new; its orbit unknown.

A few days later, the new discovery has moved from its initial point ‘z’ to ‘h’ in Angle 2. It is also a known distance from Earth. Bold verticals depict the side view of the asteroid’s disc, and line y-z is looking down the x-axis. The lines depicting the object’s size is to scale relative to their height.

Objects in the sky are measured in arcseconds, but the chart has transformed those arcseconds to millimeters. And even those aren’t exact because of page size, and on and on. However, the images are still close enough to grasp the idea of how powers of two influence the superforce over distance.

The astronomer has a good idea of the asteroid’s size at position ‘h.’ A few days later, she can determine that the size has doubled at ‘g’ and its distance traveled since ‘h’ has also doubled. According to similarity rules for triangles, at position ‘e’ its height has doubled again since discovery. Finally at ‘a’ the proportions have repeated. The positions at a, e, g, and h are all places where the objects size in the sky has increased by a factor of two. Positions under b, c, d, and f will be used to plot interim values where the distance did not double. We chose fractions of the distance from y to z for ease of plotting a graph.

That is certainly a long way to go in demonstrating how a disc’s radius grows exponentially as it approaches an observer. But it is also an important concept because as the radius of an object grows, so does its area. That is the key to understanding how effects of the superforce grow exponentially as two objects close in on each other. Since Area = πr², when the radius doubles the area quadruples. We must be careful here because r in this explanation stands for radius of image and the other r for big G refers to distance between objects.

Another graph is required to show how the distance between two objects affects the strength of the superforce acting on each body, or gravity to standard beliefs.

When the disc’s area is stacked on top of its radius it gives a better view of how much the area grows with a slight change in diameter. Vertical lines have been placed on the original marks identifying the radius at a given distance of travel in the image of Graph 1. When a curved line connects the height of each value, it forms a parabola.

As the surface of an object quadruples, its differential force also quadruples which also means that the oncoming force has increased by a factor of four.

From the graphs, we can visualize how an approaching object blocks out more and more of the background flux causing the shadow to increase by the same proportion. That is, the shadow becomes darker exponentially. This increase in turn is what produces a differential force that has quadrupled.

The above example implies that the differential force is directly proportional to the square of the radius of the approaching object. This is only a part of the alternative formula; other factors must include transparency index of both objects and other yet-to-be-determined properties.

The intent is to visualize how the area of an approaching object leads to the force increasing as distance decreases and to demonstrate why the superforce, or gravity, operates on bodies as it does, not what it does. The what has been known for hundreds of years. Understanding how superflux transparency affects the force should do that. From the preceding, we can infer that there is a correlation between gravity, mass, and superforce transparency. Those details are somewhere in the future.

Graph 2 is another curve depicting how the inverse of the closure of distance affects the radius coincides with the previous drawing. In both cases the radius of the incoming disc is dependent on the distance between, one being directly proportional to the radius; the other inversely proportional to distance between. Notice how the value on the denominator increases very rapidly as the distance closes toward contact while the direct version is relatively slower.

For ease of plotting the inverse graph, the numerator (Gm₁m₂) has been evaluated to 1,000,000, and the denominator of r² takes on values of x² because the plot is along the x axis. This looks like a parabola drawn by the curve

However, when using this equation the value of x can never get near zero. Neither can r in Newton’s equation of .

It is very upsetting when someone speaks of a person floating in a small room at the center of the earth. They reason that gravity surrounding that point cancels, and there is no more force. If the universe operated in that manner, it would probably be true. But it does not. The superforce crushes anything at Earth’s center. The total weight of any column of material in any direction will come to bare on every particle of matter in the center. And that center will continue to grow smaller and smaller, perhaps even down to a point. There will never be an empty space at that location because the superforce does not attract, it crushes.